He told me "if you ever see a 5 gallon bucket with a lid on it.

I’m going to run 1000 or so  gallons of fresh water through the cleanouts and hope for the best.

We just did a walkthrough and the house is filthy which is aggravating but it gets worse... they painted one room without ever telling us and they used the full gallon we left to repaint the room back poorly.

A five gallon bucket of Behr Marquee (what we use) costs about $200.

Invariably, if there is any paint left in a one-gallon can, I have to open it, clean the paint out of the rim and off the bottom of the lid and the reseal the can.

Not saying you have no right to bring it up, which perhaps you could and see what they counter with, most likely they will not be willing, at that point it is on you to decide whether a few gallons of paint and some sweat equity is worth it to get this home as is, currently then work to fix or if you'd rather pass because that is more important that the few gallons of paint and some sweat equity. 

We had a ten thousand gallon cistern that was filled by rain water so a whole house filtration system was a huge positive in valuing the finished property...I use quality fixtures in all my projects including rentals.

You can do that and then wait to bill back to tenants until their leases come up for renewal, but then you risk them not agreeing and moving out and now you have a vacancy.I would replace any old 1.6 gallon per flush toilets with newer 1.2s.

Soil test came out negative, but there is 300 gallons of oil left in the (abandoned) tank, so we are budgeting 10k just in case!    

I just had a new 40 gallon electric heater installed, and the technician is recommending getting a flushing service once every 3 months.Would it be worth considering a water softener for a SFH rental property?